Question: Divide the following complex numbers: $\dfrac{5 e^{2\pi i / 3}}{ e^{5\pi i / 12}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $5 e^{2\pi i / 3}$ ) has angle $\frac{2}{3}\pi$ and radius 5. The second number ( $ e^{5\pi i / 12}$ ) has angle $\frac{5}{12}\pi$ and radius 1. The radius of the result will be $\frac{5}{1}$ , which is 5. The angle of the result is $\frac{2}{3}\pi - \frac{5}{12}\pi = \frac{1}{4}\pi$ The radius of the result is $5$ and the angle of the result is $\frac{1}{4}\pi$.